Hundreds of Market Basket workers demonstrated outside the company's headquarters Monday, the day the company had set as a deadline for thousands of Market Basket workers to return to work or be replaced.

The company's board of directors quickly dismissed an offer from ousted Market Basket CEO Arthur T. Demoulas who offered to return to work and bring his previous management team while he continues to negotiate to buy the company from rival family members.

"These steps are critical at this point and are in the best interests of associates, customers, vendors and shareholders," a public relations firm working on his behalf said.

Workers are planning a major rally in Tewksbury Tuesday, the day after management’s deadline.

"Arthur T. has also offered to move immediately to return to work in advance of the completion of the stock purchase and work to bring back his full team to stabilize and begin to restore the business," the statement said.

The offer was rejected within hours after it was made Sunday night.

"The board fully supports the current management team in their efforts to ensure that Market Basket’s normal business operations resume immediately for the benefit of its customers, associates, vendors and communities," a statement said.

Business has been significantly down in recent weeks as workers protest Arthur T. Demoulas' firing and leave shelves empty.

"The customers chose not to shop here in support of what we’re doing because they want Market Basket to stay the same," said Lisa Adams, who works in the bakery at the Burlington store. "Because there’s no customers that means no work, no pay."

The grocery chain has 71 stores in Massachusetts, New Hampshire and Maine.